Find the sum of first 10 even natural numbers.

Answer

To find the sum of the first 10 even natural numbers, we can use the concept of Arithmetic Progression (AP).

### Step-by-Step Solution:

1. **Identify the first 10 even natural numbers**:
The first 10 even natural numbers are: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20.

2. **Determine the first term (A) and the common difference (D)**:
- The first term (A) is 2.
- The common difference (D) can be calculated as the difference between the second term and the first term:
\[ D = 4 - 2 = 2. \]

3. **Use the formula for the sum of the first n terms of an AP**:
The formula for the sum of the first n terms (S_n) of an AP is given by:
\[ S_n = \frac{n}{2} \times (2A + (n - 1)D) \]
where:
- \( n \) is the number of terms,
- \( A \) is the first term,
- \( D \) is the common difference.

4. **Substitute the values into the formula**:
Here, \( n = 10 \), \( A = 2 \), and \( D = 2 \).
\[ S_{10} = \frac{10}{2} \times (2 \times 2 + (10 - 1) \times 2) \]

5. **Calculate the expression**:
- First, calculate \( \frac{10}{2} = 5 \).
- Next, calculate \( 2 \times 2 = 4 \).
- Then, calculate \( (10 - 1) \times 2 = 9 \times 2 = 18 \).
- Now, combine these: \( 4 + 18 = 22 \).
- Finally, multiply: \( 5 \times 22 = 110 \).

6. **Conclusion**:
The sum of the first 10 even natural numbers is **110**.